There are a multiplicity of applications in which it is necessary to vary the frequency of a given digital equidistant time signal by means of digital filtering. Interpolation filters are used as component circuits in digital switching systems in which a change in the sampling frequency of digital signals is necessary. Systems that are concerned only with simple integral sampling frequency ratios are not the subject matter of the invention.
Methods for arbitrarily changing sampling frequencies are described in “IEEE, Transactions of Acoustics, Speech and Signal Processing”, Volume ASSP-32, No. 3, July 1984, pages 577–591 under the title of “Digital Methods for Conversion between Arbitrary Sampling Frequencies”, author: T. A. Ramstad. The associated circuits are denoted as hybrid systems that consist of a first interpolation filter with a fixed sampling frequency ratio, and a second interpolation filter. The second interpolation filter determines intermediate values that lie arbitrarily in time between the fixed samples of the sampling lattice downstream of the second interpolation filter, and thus permit arbitrary sampling frequency ratios. The first interpolation filter includes an interpolation device and a digital filter as a combination. The interpolation device, which is also denoted as an oversampling device, is used to insert “0” values between the original samples in accordance with an oversampling factor N. A downstream digital filter is the first to smooth the variation in the digital samples, the signal jumps to the 0 values, in particular, being compensated such that the spectrum of the useful signal is not falsified by higher frequency components. The first interpolation filter is designed for this purpose such that relatively large frequency band gaps are formed in the infinitely extending frequency spectrum. It holds in the case of oversampling as well that the frequency spectra are reflected at half the original sampling frequency and multiples thereof. However, a new sampling frequency that forms an integral frequency ratio with the original sampling frequency is to be assumed downstream of the interpolation device and of the digital filter. The digital filter in this case removes the remaining spectral components between the useful signal band and the reflected frequency band in the case of the new sampling frequency and the associated frequency multiples. The digital filter functions in this case simply as a digital lowpass filter that passes the useful signal frequency band and suppresses the frequency components thereabove. In this case, however, a reflection occurs at half the sampling frequency in accordance with the sampling theorem. It follows that a digital lowpass filter cannot suppress the multiples of the sampling frequency.
The spectral signal components in the new sampling frequency and the frequency multiples must be suppressed for the implementation of arbitrary sampling frequency ratios. If these signal interference components are not suppressed, signal interference components occur in the useful signal frequency band during the generation of arbitrary sampling frequency ratios. The first interpolation filter is described in “Proceedings of the IEEE”, Volume 61, No. 6, June 1973, pages 692–702, and in the article by R. W. Schafer and L. R. Rabbiner entitled “A Digital Signal Processing Approach to Interpolation”.
A method having a hybrid system for sampling frequency conversion is disclosed in EP-A-0 561 067. This system operates with an oversampling factor of N=2, and therefore achieves only a relatively poor signal-to-noise ratio. This poor signal-to-noise ratio is tolerable in the case of this hybrid system since it is used for video signal applications. A second interpolation filter is implemented as a lowpass filter that suppresses all signal components whose frequencies are greater than 1.5 times the value of the original sampling frequency. The analog lowpass response is achieved with the aid of a transverse filter in the case of which the weighting factors of the stored samples depend on a time difference value. Such a lowpass filter suppresses in this case not only the remaining spectral signal components in the frequency multiples of the new sampling frequency, but the entire frequency spectral region above a blocking edge. Although having a comparable transmitting/blocking characteristic, in comparison with a corresponding comb filter arrangement such a lowpass filter can be implemented only at great expense.
The “Journal of Audio Engineering Society”, Volume 41, No. 7/8, 1993, pages 539–555 by R. Adams and T. Corn entitled “Theory and VLSI Architectures for Asynchronous Sample Rate Converters” describes a method for a sampling frequency conversion system that treats the use of relatively simple sample-and-hold circuits, on the one hand, and the use of lowpass filters as analog resamplers, on the other hand.
After the N-fold oversampling and filtering there are present in each case in the frequency spectrum downstream of the first interpolation filter in the abovenamed systems interference signal frequency bands whose center frequencies are at the frequency multiples of the new sampling frequency. The frequency bandwidth of each signal interference region is equal in this case to double the frequency bandwidth of the useful signal. If the Nyquist condition for the original digitization is fulfilled, the frequency bandwidth of the interference signal region exhibits in the limiting case at most the value of the original sampling frequency. The position and bandwidth of all the interference regions are defined in the frequency spectrum by the original sampling frequency and the original oversampling factor N. The N-fold oversampling of the original digital sampling frequency has the effect that the relative frequency bandwidth of the interference signal regions in the frequency spectrum is reduced by the factor of 1/N referred to the new sampling frequency. This facilitates the separation of the useful signal frequency band from the respective interference signal frequency region, since the transition region between the transmission and the blocking frequency band for the second interpolation filter is enlarged. This reduces the outlay on circuitry required for the second interpolation filter. However, the price for this is a higher outlay on circuitry for the smoothing filter in the first interpolation filter. There is therefore either a need for a very complicated first interpolation filter and a simple second interpolation filter, for example a linear interpolator, or there is a simple first interpolation filter, for example with a very small oversampling, and a very complicated lowpass filter with the aid of which the analog resampler is implemented.